understanding m values, Nurkowanie, Teoria dekompresji [ Pobierz całość w formacie PDF ]
Understanding M-values
By Erik C. Baker, P.E.
In conjunction with an array of hypothetical "tissue" compartments, gas loading calculations and
M-values compose the major elements of the dissolved gas or "Haldanian" decompression model.
Through the use of widely-available desktop computer programs, technical divers rely on this
model for their decompression safety. A good understanding of M-values can help divers to
determine appropriate conservatism factors and evaluate the adequacy of various decompression
profiles for a particular dive.
hat are M-values? The term
"M-value" was coined by
Robert D. Workman in the
mid-1960's when he was doing
decompression research for the U.S.
Navy Experimental Diving Unit
(NEDU). Workman was a medical
doctor with the rank of Captain in the
Medical Corps of the U.S. Navy.
The "M" in M-value stands for
"Maximum." For a given ambient
pressure, an M-value is defined as the
maximum value of inert gas pressure
(absolute) that a hypothetical "tissue"
compartment can "tolerate" without
presenting overt symptoms of
decompression sickness (DCS). M-
values are representative limits for the
tolerated gradient between inert gas
pressure and ambient pressure in each
compartment. Other terms used for
M-values are "limits for tolerated
overpressure," "critical tensions," and
"supersaturation limits." The term M-
value is commonly used by
decompression modelers.
without experiencing symptoms of DCS.
Because the ambient pressure at 33 fsw
depth is twice that at sea level, Haldane
concluded that a ratio of 2:1 for tolerated
overpressure above ambient could be
used as the ascent limiting criteria. This
approximate ratio was used by Haldane to
develop the first decompression tables.
In later years, and up until the 1960's,
other ratios were used by various
modelers for the different half-time
compartments. Most of the U.S. Navy
decompression tables were calculated
using this supersaturation ratio method.
However, there was a problem. Many
of the tables produced by this method
were deficient when it came to deeper
and longer dives. Robert Workman
began a systematic review of the
decompression model including previous
research that had been performed by the
U.S. Navy. He arrived at some
important conclusions. First of all, he
recognized that Haldane's original ratio
of 2:1 (based on air) was really a ratio of
1.58:1 if you considered only the partial
pressure of the inert gas in air - nitrogen.
[By that time in decompression research
it was known that oxygen was not a
significant factor in DCS; it was the inert
gases like nitrogen and helium that were
the culprits.] In his review of the research
data, Workman found that the "tissue
ratios" for tolerated overpressure varied
by half-time compartment and by depth.
The data showed that the faster half-time
compartments tolerated a greater
overpressure ratio than the slower
compartments, and that for all
compartments the tolerated ratios became
less with increasing depth. Then, instead
of using ratios, Workman described the
maximum tolerated partial pressure of
nitrogen and helium for each
compartment at each depth as the "M-
value." Next, he made a "linear
projection" of these M-values as a
function of depth and found that it was a
reasonably close match to the actual data.
He made the observation that "a linear
projection of M-values is useful for
computer programming as well."
THE WORKMAN M-VALUES
Workman's presentation of M-values in
the form of a linear equation was a
significant step in the evolution of the
dissolved gas decompression model. His
M-values established the concept of a
linear relationship between depth
pressure [or ambient pressure] and the
tolerated inert gas pressure in each
"tissue" compartment. This concept is an
important element of the present-day
dissolved gas model as applied by a
variety of modelers.
Workman expressed his M-values in
the slope-intercept form of a linear
equation (see Figure 1). His surfacing
value was designated M
O
[pronounced
"M naught"]. This was the intercept
value in the linear equation at zero depth
pressure (gauge) at sea level. The slope
in the linear equation was designated
HISTORICAL BACKGROUND
In the dissolved gas or "Haldanian"
decompression model, gas loading
calculations for each hypothetical "tissue"
compartment are compared against
"ascent limiting criteria" to determine the
safe profile for ascent. In the early years
of the model, including the method
developed by John S. Haldane in 1908,
the ascent limiting criteria was in the
form of "supersaturation ratios." For
example, Haldane found that a diver
whose "tissues" were saturated by
breathing air at a depth of 33 fsw could
ascend directly to the surface (sea level)
M [pronounced "delta M"] and
represented the change in M-value with
change in depth pressure.
THE BÜHLMANN M-VALUES
Professor Albert A. Bühlmann, M.D.,
began doing decompression research in
1959 in the Laboratory of Hyperbaric
Physiology at the University Hospital in
Zürich, Switzerland. Bühlmann
1
continued his research for over thirty
years and made a number of important
contributions to decompression science.
In 1983 he published the first edition (in
German) of a successful book entitled
Decompression - Decompression
Sickness
. An English translation of the
book was published in 1984.
Bühlmann’s book was the first nearly
complete reference on making
decompression calculations that was
widely-available to the diving public. As
a result, the "Bühlmann algorithm"
became the basis for most of the world’s
in-water decompression computers and
do-it-yourself desktop computer
programs. Three more editions of the
book were published in German in 1990,
1993, and 1995 under the name
Tauchmedizin
or "Diving Medicine." [An
English translation of the 4th Edition of
the book (1995) is in preparation for
publication].
Bühlmann’s method for
decompression calculations was similar
to the one that Workman had prescribed.
This included M-values which expressed
a linear relationship between ambient
pressure and tolerated inert gas pressure
in the hypothetical "tissue"
compartments. The major difference
between the two approaches was that
Workman’s M-values were based on
depth pressure (i.e. diving from sea level)
and Bühlmann’s M-values were based on
absolute pressure (i.e. for diving at
altitude). This makes sense, of course,
since Workman was concerned with the
diving activities of the U.S. Navy
(presumably performed at sea level)
while Bühlmann was concerned with
diving activities in the high mountain
lakes of Switzerland.
Bühlmann published two sets of M-
values which have become well-known in
diving circles; the ZH-L
12
set from the
1983 book, and the ZH-L16 set(s) from
the 1990 book (and later editions). The
"ZH" in these designations stands for
"Zürich" (named after his hometown),
the "L" stands for "linear," and the "12"
or "16" represents the number of pairs of
coefficients (M-values) for the array of
half-time compartments for helium and
nitrogen. The ZH-L
12
set has twelve
pairs of coefficients for sixteen half-time
compartments and these M-values were
determined empirically (i.e. with actual
Pressure Graph: Workman-style M-values
versus Bühlmann-style M-values
y
y
y
x
x
slope = 1.0
Workman M =
slope
Workman M = intercept at
zero depth pressure (gauge)
O
y
x
Bühlmann Coefficient b =
reciprocal of slope (1/b = slope)
Bühlmann Coefficient a = intercept at
zero ambient pressure (absolute)
0
0
x
Ambient Pressure, absolute
Figure 1
decompression trials). The ZH-L16A set
has sixteen pairs of coefficients for
sixteen half-time compartments and these
M-values were mathematically-derived
from the half-times based on the tolerated
surplus volumes and solubilities of the
inert gases. The ZH-L16A set of M-
values for nitrogen is further divided into
subsets B and C because the
mathematically-derived set A was found
empirically not to be conservative enough
in the middle compartments. The
modified set B (slightly more
conservative) is suggested for table
calculations and the modified set C
(somewhat more conservative) is
suggested for use with in-water
decompression computers which
calculate in real-time.
Similar to the Workman M-values,
the Bühlmann M-values are expressed in
the slope-intercept form of a linear
equation (see Figure 1). The Coefficient
a
is the intercept at zero ambient pressure
(absolute) and the Coefficient
b
is the
reciprocal of the slope. [Note: the
Coefficient
a
does not imply that humans
can withstand zero absolute pressure!
This is simply a mathematical
requirement for the equation. The lower
limit for ambient pressure in the
application of the Bühlmann M-values is
on the order of 0.5 atm/bar.]
DCAP AND DSAT M-VALUES
Many technical divers will recognize the
11F6 set of M-values used by Hamilton
Research’s Decompression Computation
and Analysis Program (DCAP). This set
or "matrix" of M-values was determined
by Dr. Bill Hamilton and colleagues
during development of new air
decompression tables for the Swedish
Navy. In addition to air diving, the 11F6
M-values have worked well for trimix
diving and are the basis for many custom
decompression tables in use by technical
divers.
Many sport divers are familiar with
2
the Recreational Dive Planner (RDP)
distributed by the Professional
Association of Diving Instructors
(PADI). The M-values used for the RDP
were developed and tested by Dr.
Raymond E. Rogers, Dr. Michael R.
Powell, and colleagues with Diving
Science and Technology Corp. (DSAT),
a corporate affiliate of PADI. The DSAT
M-values were empirically verified with
extensive in-water diver testing and
Doppler monitoring.
determined by various independent
researchers around the globe. This is a
good sign as it indicates that the science
has determined a relatively consistent
threshold for symptoms of decompression
sickness across the human population.
Workman Definitions:
M = tolerated inert gas pressure
(absolute) in hypothetical
"tissue" compartment
Depth = depth pressure (gauge)
measured from surface at sea
level
Tolerated Depth = tolerated depth
pressure (gauge) measured from
surface at sea level
FORMAT FOR M-VALUES
M-values are often expressed in the form
of a linear equation as in the Workman-
style or the Bühlmann-style. This format
is ideal for computer programming since
it allows the M-values to be calculated
"on-the-fly" as they are needed. The
linear format permits the display of M-
value lines on the pressure graph as well.
M-values can also be expressed in the
form of a "matrix" or table. This is
simply where the M-values for each half-
time compartment and each stop depth
are pre-calculated and arranged in
columns and rows. This format is useful
for detailed comparisons and analysis.
Some of the early dive computers and
desktop computer programs used the
table format to "look up" M-values for
each stop during the calculation process.
M = intercept at zero depth
pressure (gauge); surfacing
M-value
M = slope of M-value line
O
COMPARISON OF M-VALUES
Tables 1 thru 4 present a comparison of
M-values for nitrogen and helium
between the various Haldanian
decompression algorithms discussed in
this article. All M-values are presented
in Workman-style format. An evolution
or refinement in the M-values is evident
from Workman (1965) to Bühlmann
(1990). The general trend has been to
become slightly more conservative. This
trend reflects a more intensive validation
process (empirical testing) and includes
the use of Doppler ultrasound monitoring
for the presence and quantity of "silent
bubbles" (bubbles which are detectable in
the circulation but are not associated with
overt symptoms of decompression
sickness).
Bühlmann Definitions:
P i.g. = tolerated inert gas
pressure (absolute) in hypothetical
"tissue" compartment
t.tol.
P i.g. = inert gas pressure
(absolute) in hypothetical "tissue"
compartment
t.
P = ambient pressure (absolute)
amb.
P = tolerated ambient
amb.tol.
pressure (absolute)
a = intercept at zero ambient
pressure (absolute)
b = reciprocal of slope of
M-value line
M-VALUE CHARACTERISTICS
M-value sets can be classified into two
categories, no-decompression sets and
decompression sets. No-decompression
M-values are surfacing values only. The
DSAT RDP M-values are an example.
No-stop dive profiles are designed so that
the calculated gas loadings in the
compartments do not exceed the
surfacing M-values. This allows for
direct ascent to the surface at any time
during the dive. Some no-decompression
CONSISTENCY OF M-VALUES
algorithms account for ascent and
descent rates in the calculations.
One observation that can be made about
the comparison between the M-values of
the various algorithms is that there is not
a great difference between them. In other
words, there appears to be a certain
consistency between the values
3
 Table 1: Comparison of M-values for Nitrogen Between Various Haldanian Decompression Algorithms
American System of Pressure Units - feet of sea water (fsw)
Workman
M-values (1965)
Bühlmann ZH-L
M-values (1983)
DSAT RDP
M-values (1987)
DCAP MF11F6
M-values (1988)
Bühlmann ZH-L16
M-values (1990)
12
A
B
C
Cpt
No.
HT
min
M
fs
O
M
Cpt
No.
HT
min
M
fs
O
M t
No.
HT
min
M
fs
O
Cpt
No.
HT
M
fs
O
M
slope
Cpt
No.
HT
min
M
fs
O
M
M
M
O
fsw
O
fsw
slope
slope
min
slope
1
2.65
111.9
1.2195
1
4.0
106.4
106.4
106.4
1.9082
1
5
104
1.8
1
5
99.08
1
2
5
10
104.0
80.5
1.30
1b
5.0
97.3
97.3
97.3
1.7928
2
10
88
1.6
2
7.94
89.1
1.2195
2
10
82.63
1.05
2
8.0
83.2
83.2
83.2
73.8
66.8
1.5352
3
4
12.2
18.5
75.2
68.8
1.2121
3
4
12.5
18.5
73.8
73.8
1.3847
3
20
72
1.5
1.1976
3
4
20
66.89
66.8
66.8
1.2780
5
26.5
63.5
1.1834
30
59.74
3
25
62.3
1.08
5
27.0
62.3
62.3
60.8
1.2306
4
40
56
1.4
6
37
57.3
1.1628
5
40
55.73
6
38.3
58.5
57.4
55.6
1.1857
7
8
53
79
53.2
51.9
1.1494
6
60
80
51.44
49.21
4
55
48.6
1.06
7
8
54.3
77.0
55.2
54.1
52.3
1.1504
5
80
54
1.3
1.1236
7
8
52.3
51.7
50.1
1.1223
100
47.85
5
95
45.4
1.04
9
109
49.9
49.9
48.5
1.0999
6
120
52
1.2
9
114
51.9
1.1236
9
120
46.93
7
8
160
200
51
1.15
1.1
10
11
146
185
50.2
50.2
1.0707
10
11
160
200
45.78
45.07
6
7
145
200
44.7
44.1
1.02
10
11
146
187
48.2
48.2
47.2
46.1
1.0844
51
1.0707
1.01
46.8
46.8
1.0731
9
240
50
1.1
12
238
47.3
1.0593
12
240
44.60
12
239
45.6
45.6
45.1
1.0635
13
304
42.6
1.0395
8
285
44.0
1.0
13
305
44.5
44.1
44.1
1.0552
14
15
397
503
42.6
42.6
1.0395
13
360
480
43.81
43.40
9
10
385
520
44.0
44.0
1.0
14
15
390
498
43.5
43.5
43.1
42.4
41.8
1.0478
1.0395
14
1.0
42.6
42.6
1.0414
16
635
42.6
1.0395
16
635
41.8
41.8
1.0359
670
43.5
1.0
11
Cpt = Compartment HT = Half-time M = Surfacing M-value (sea level = 1 atm = 33 fsw = 1.01325 bar) M = slope of M-value line
O
Table 2: Comparison of M-values for Nitrogen Between Various Haldanian Decompression Algorithms
European System of Pressure Units - meters of sea water (msw)
Workman
Bühlmann ZH-L
M-values (1983)
DSAT RDP
DCAP MM11F6
Bühlmann ZH-L16
12
M-values (1965)
M-values (1987)
M-values (1988)
M-values (1990)
A
B
C
Cpt
HT
M
M
Cpt
HT
M
M
Cpt
HT
min
M
Cpt
HT
M
M
Cpt
HT
M
M
msw
M
M
O
O
O
O
O
O
O
No.
min
msw
slope
No.
min
2.65
msw
slope
No.
msw
No.
min
msw
slope
No.
min
msw
msw
slope
1
34.2
1.2195
1
4.0
32.4
32.4
32.4
1.9082
1
5
31.7
1.8
1
5
30.42
1
5
31.90
1.30
1b
5.0
29.6
29.6
29.6
1.7928
2
10
26.8
1.6
27. 4
27.2
1.2195
2
10
25.37
2
10
24.65
1.05
2 .0
25.4
25.4
22.5
25.4
22.5
1.5352
3
12.2
22.9
1.2121
3 .5
22.5
1.3847
3
20
21.9
1.5
4
5
18.5
21.0
19.3
1.1976
1.1834
3
4
20
20.54
18.34
4 .5
5 7.0
20.3
19.0
20.3
20.3
1.2780
1.2306
26.5
30
3
25
19.04
1.08
19.0
18.5
4
40
17.0
1.4
6
37
17.4
1.1628
5
40
60
17.11
6
38.3
17.8
17.5
16.9
1.1857
7
53
79
16.2
1.1494
6
15.79
4
55
14.78
1.06
7
54.3
16.8
16.5
15.7
15.9
15.2
1.1504
5
80
16.4
1.3
8
15.8
1.1236
7
8
9
80
15.11
14.69
14.41
8
77.0
15.9
15.2
1.1223
100
5
95
13.92
1.04
9
109
15.2
14.7
1.0999
6
120
15.8
1.2
9
114
15.8
1.1236
120
7
160
200
15.5
1.15
1.1
10
11
146
15.3
1.0707
1.0707
10
11
160
14.06
13.84
6
7
145
200
13.66
1.02
1.01
10
146
14.6
14.2
14.6
14.2
14.3
14.0
1.0844
8
15.5
185
15.3
200
13.53
11
187
1.0731
9
240
15.2
1.1
12
13
238
14.4
12.9
1.0593
1.0395
12
240
13.69
12
239
13.9
13.5
13.9
13.7
1.0635
304
8
285
13.50
1.0
13
305
13.4
13.4
1.0552
14
397
12.9
1.0395
13
360
480
13.45
13.33
9
385
520
13.50
1.0
14
390
13.2
13.2
13.1
1.0478
15
503
635
12.9
1.0395
14
10
13.40
1.0
15
498
12.9
12.9
12.7
12.9
12.7
1.0414
16
12.9
1.0395
16
635
12.7
1.0359
11
670
13.30
1.0
Cpt = Compartment HT = Half-time M = Surfacing M-value (sea level = 10 msw = 1.0 bar) M = slope of M-value line
O
4
 Decompression M-values are
characterized by having a slope
parameter which determines the change
in M-value with change in ambient
pressure. The value of the slope
parameter will vary depending on the
half-time of the hypothetical "tissue"
compartment. Generally, faster half-time
compartments will have a greater slope
than slower half-time compartments.
This reflects the observation that faster
compartments tolerate greater
overpressure than slower compartments.
If the slope is greater than 1.0 then the
M-value line "expands" on the pressure
graph and that compartment will tolerate
greater overpressure gradients with
increasing depth. A fixed slope of 1.0
means that the compartment will tolerate
the same overpressure gradient regardless
of depth. In all cases, the value of the
slope can never be less than 1.0.
Otherwise, the M-value line would cross
under the ambient pressure line at some
point and this would represent an
"illogical" situation whereby the
compartment could not tolerate even the
ambient pressure.
Table 3: Comparison of M-values for Helium
Between Various Haldanian Decompression Algorithms
American System of Pressure Units - feet of sea water (fsw)
Workman
M-values (1965)
Bühlmann ZH-L
M-values (1983)
Bühlmann ZH-L16A
M-values (1990)
12
Cpt
No.
HT
min
M
fsw
M
Cpt
No.
HT
min
M
fsw
M t
No.
HT
min
M
fsw
M
O
O
O
slope
slope
slope
1
1.0
111.9
1.2195
1
1.51
134.5
2.3557
1b
1.88
121.9
2.0964
2
3.0
89.1
1.2195
2
3.02
102.5
1.7400
1
5
86
1.5
3
4
4.6
7.0
75.2
68.8
1.2121
3
4
4.72
6.99
89.4
1.5321
1.1976
79.7
1.3845
2
10
74
1.4
5
10
63.5
1.1834
5
10.21
73.6
1.3189
6
14
57.3
1.1628
6
14.48
68.2
1.2568
3
20
66
1.3
7
8
20
30
53.2
51.9
1.1494
7
8
20.53
29.11
63.7
1.2079
1.1236
59.8
1.1692
4
40
60
1.2
9
43
51.9
1.1236
9
10
11
41.20
55.19
70.69
57.1
1.1419
10
11
55
70
52.4
52.4
1.0799
55.1
1.1232
5
80
56
1.2
1.0799
1.0799
1.0799
1.0799
1.0799
1.0799
54.0
1.1115
12
90
52.4
12
90.34
53.3
1.1022
6
120
54
1.2
13
115
52.4
13
115.29
53.1
1.0963
7
8
160
200
54
1.1
1.0
14
15
150
190
52.4
52.4
14
15
147.42
188.24
52.8
1.0904
53
52.6
1.0850
9
240
53
1.0
16
240
52.4
16
240.03
52.3
1.0791
Cpt = Compartment HT = Half-time M = slope of M-value line
M = Surfacing M-value (sea level = 1 atm = 33 fsw = 1.01325 bar)
O
THE AMBIENT PRESSURE LINE
Table 4: Comparison of M-values for Helium
Between Various Haldanian Decompression Algorithms
The ambient pressure line is an all-
important reference line on the pressure
graph. Passing through the origin, it has
a slope of 1.0 and simply represents the
collection of points where the
compartment inert gas loading will be
equal to ambient pressure. This is
important because when the inert gas
loading in a compartment goes above the
ambient pressure line, an overpressure
gradient is created. An M-value line
represents the established limit for
tolerated overpressure gradient above the
ambient pressure line.
European System of Pressure Units - meters of sea water (msw)
Workman
Bühlmann ZH-L
Bühlmann ZH-L16A
M-values (1990)
12
M-values (1965)
Cpt
No.
M-values (1983)
HT
min
M
O
msw slope
M
Cpt
No.
HT
M
M
t
HT
min
M
O
M
O
min
1 .0
msw
slope
No.
msw
slope
34.2
1.2195
1
1.51
41.0
37.2
31.2
2.3557
1b
1.88
2.0964
2 .0
27.2
1.2195
1.2121
1.1976
2
3.02
1.7400
1
5
26.2
1.5
3
4.6
22.9
3
4.72
27.2
1.5321
4 .0
21.0
4
6.99
24.3
1.3845
1.3189
1.2568
1.2079
1.1692
1.1419
1.1232
1.1115
1.1022
1.0963
1.0904
1.0850
1.0791
2
10
22.5
1.4
5 0
6 4
19.3
17.4
1.1834
5
6
10.21
22.4
20.8
1.1628
1.1494
1.1236
14.48
3
20
20.1
1.3
7
20
16.2
7
20.53
19.4
THE DECOMPRESSION ZONE
8 0
15.8
8
29.11
18.2
4
40
18.3
1.2
9 3
15.8
15.9
1.1236
1.0799
1.0799
1.0799
1.0799
1.0799
1.0799
1.0799
9
41.20
17.4
The "decompression zone" is the region
on the pressure graph between the
ambient pressure line and the M-value
line (see Figure 3). Within the context of
the dissolved gas model, this zone
represents the functional area in which
decompression takes place. In theory, a
positive gradient above ambient pressure
is desireable in order for a compartment
to "off-gas" or "decompress." In some
10
55
10
11
55.19
16.8
5
80
17.0
1.2
11
70
15.9
15.9
15.9
15.9
15.9
15.9
70.69
16.4
12
90
12
90.34
16.2
6
120
16.4
1.2
13
115
13
14
15
115.29
16.1
7
8
160
16.4
16.1
1.1
1.0
14
15
150
190
147.42
16.1
16.0
200
188.24
9
240
16.1
1.0
16
240
16
240.03
15.9
Cpt = Compartment HT = Half-time M = slope of M-value line
M = Surfacing M-value (sea level = 10 msw = 1.0 bar)
O
5
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